Stability and Control — Page 280, Lesson 334

Let's pick up with the manoeuvring stick force gradient, because that's where the real meat of this section sits. I want you to think of it this way: when you pull back on the stick to generate a load factor, the force you feel in your hand is the stick force gradient. And that gradient is directly tied to the static stability of the aeroplane. Here's the key relationship: when the aeroplane has high static stability, the manoeuvring stability will be high, and that produces a high stick force gradient. So the more stable the aircraft, the more force you need per unit of load factor. Now, there's a real design consequence here. A possibility exists that the forward CG limit could be set specifically to prevent an excessively high manoeuvring stick force gradient. In other words, the forward CG limit isn't just about stability — it's also there to keep the stick forces from becoming too heavy for the pilot to handle. Now, as the CG moves aft, the stick force gradient decreases, because manoeuvring stability is decreasing. And here's the flip side: the lower limit of stick force gradient may be reached. So you have a band — too far forward and the gradient is too high, too far aft and it drops too low. The CG envelope is bounded by both. There's a calculation note here that I want you to remember, because it's a classic trap. When you're asked to calculate "stick force per g", remember that the aircraft is at 1g to start with. So you must subtract 1g from the "g" limit before dividing by the pull force. Let me say that again slowly: the aircraft is already at 1g in straight and level flight. If you pull to 3g, the change in load factor is only 2g. So you divide the pull force by (n minus 1), not by n. That's the correction. Now, pitch damping. The pitch damping of the aeroplane is related to air density. At high altitudes, the high TAS — true airspeed — reduces the change in tail angle of attack for a given pitching velocity, and that reduces the pitch damping. So the physical picture is: when the aircraft pitches, the tail moves through the air, and that generates a damping moment. At high altitude, the air is less dense, but the TAS is higher for the same indicated speed. The higher TAS means that for a given angular pitching velocity, the change in angle of attack at the tail is smaller. Less change in angle of attack means less damping force. So you can expect a decrease in manoeuvring stick force stability with increased altitude. That's a direct consequence. Now let's move to tailoring control forces. The principle here is that control forces should reflect the stability of the aeroplane, but at the same time they should be of a tolerable magnitude. So you can't just let the forces be whatever physics dictates — you have to shape them. A manual flying control system may employ an infinite variety of techniques to provide satisfactory control forces throughout the speed, CG, and altitude range of the aircraft. That's the design goal. The first technique is the stick centring spring. If a spring is added to the control system, it will tend to centre the stick and provide a force increment depending on stick displacement. So the further you move the stick from centre, the more force the spring adds. Now, when the control system has a fixed gearing between stick position and surface deflection, the centring spring provides a contribution to stick force stability according to stick position. Here's the important part: the contribution to stick force stability will be largest at low flight speeds, where relatively large control deflections are required. And it will be smallest at high airspeed, because of the smaller control deflections required. So the spring's effect is speed-dependent — it helps most when you're slow and need big deflections, and helps least when you're fast and only need small deflections. The net effect: the stick centring spring increases the airspeed and manoeuvring stick force stability, but the contribution decreases at high airspeeds. There's a variation of this device: a spring stiffness controlled to vary with dynamic pressure — that's the "Q-Feel" system. In that case, the contribution of the spring to stick force stability would not diminish with speed. Because the spring stiffness itself is being adjusted with dynamic pressure, it compensates for the reduced deflection at high speed. Now the down spring. A down spring added to a control system is a means of increasing airspeed stick force stability without a change in aeroplane static stability. That's a crucial distinction — it changes the stick force feel, but it does not change the actual static stability of the aircraft. As shown in Figure 10.41, a down spring consists of a long pre-loaded spring attached to the control system which tends to rotate the elevators down — that's aircraft nose-down. The effect of the down spring is to contribute an increment of pull force independent of control deflection or airspeed. So unlike the centring spring, which depends on displacement, the down spring gives you a constant pull-force increment regardless of how far you move the stick or how fast you're flying. That's what makes it useful for tailoring the force feel at high speed without altering the stability characteristics.